Riley Clark
01/07/2023 · Senior High School
Write an equation of the circle with center \( (-8,-4) \) and diameter 10 . \( \square \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To write the equation of a circle, we can use the standard form of the equation of a circle, which is given by:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
Given the center of the circle \((-8, -4)\) and a diameter of 10, we first need to find the radius. The radius \(r\) is half of the diameter:
\[
r = \frac{10}{2} = 5
\]
Now we can substitute the center \((-8, -4)\) and the radius \(5\) into the equation:
\[
(x - (-8))^2 + (y - (-4))^2 = 5^2
\]
This simplifies to:
\[
(x + 8)^2 + (y + 4)^2 = 25
\]
Thus, the equation of the circle is:
\[
\boxed{(x + 8)^2 + (y + 4)^2 = 25}
\]
Quick Answer
The equation of the circle is \((x + 8)^2 + (y + 4)^2 = 25\).
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit